A note on the maximum deviation of the scale-contaminated normal to the best normal distribution

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• 作者：Dankmar B?hning and Roumporn Ruangroj
• 关键词：Key words ; mixture of normals with different component variances ; scale ; contaminated normal ; maximum deviation ; suprenum's norm
• 刊名：Metrika
• 出版年：2002
• 出版时间：June 2002
• 年：2002
• 卷：55
• 期：3
• 页码：177-182
• 全文大小：63 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1435-926X

文摘

In this paper we consider the case of the scale-contaminated normal (mixture of two normals with equal mean components but different component variances: (1?p)N(μ,σ2)+pN(μ,τ2) with σ and τ being non-negative and 0≤p≤1). Here is the scale error and p denotes the amount with which this error occurs. It's maximum deviation to the best normal distribution is studied and shown to be montone increasing with increasing scale error. A closed-form expression is derived for the proportion which maximizes the maximum deviation of the mixture of normals to the best normal distribution. Implications to power studies of tests for normality are pointed out.